if we take a normal lottery yes
Lets say its like loot rolls in dutys and add an additonal 5 for every time you failed to win a house and people trying either long time would get a higher chance or people with enought money to roll for multiple houses at once (lets say we pay upfront and get money back when you lose) could boost there chances considerable you still would have to wait/grind for houses but you could at least do something with your time